A fully nunlinear numerical wave tank (NWT) has been simulated by use of a three dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these ap proaches has a high accuracy and good numerical stability.

A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to estab-lish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping lay-er is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the meth-od is used to compute the second-order wave forces and runup on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.

The paper provides a detailed analysis for the second-order diffraction of monochromatic waves. For the second-order potential on the free surface, the paper proposed a forward prediction method for computing the integration on the free surface. By this method we only need to run the infinity integration on the free surface directly for a few points; a one-step quadrature can then be applied successively outward from the body for potentials at other points. For wave diffraction from a body of revolution with a vertical axis, the paper derives a new integral equation, which can cancel the leading singularity in the derivative of ring Green’s functions automatically. To obtain accurate results, different approaches are also used to deal with singularities in the ring Green’s functions in the integration on both the body surface and free surface. The method has been implemented for bodies of revolution with vertical axes, but the theory is also available for arbitrary bodies. A numerical examination is made to validate the numerical code by comparing the secondorder forces and moments on uniform and truncated cylinders and second-order diffraction potentials on the free surface with some published results. The comparison shows that the present results are in good agreement with those published. The method is also used to compute the second-order wave elevation around uniform and truncated cylinders. Ó 1998 Elsevier Science Ltd. All rights reserved.

A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave sur-face elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial deriva-tives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor-corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in litera-ture. The comparison demonstrates that the new form of the equations is capable of calcu-lating wave transformation from relative deep water to shallow water.

Within the frame of potential theory and the assumption of weak nonlinearity of wave motion, a numerical method is developed for the third-order triple-frequency wave loads on fixed axisymmetric bodies in monochromatic incident waves. Applying the numerical code, numerical computations were carried out for surge and heave forces and pitch moments on a uniform cylinder, truncated cylinders and a hemisphere. Examinations were made of the contribution to third-order forces and moments from potentials at each wave order, and the relation of third-order forces and moments to wave number and drafts of cylinders.

Within the frame of potential theory and the assumption of weak nonlinearity of wave motion, a numerical method is developed for the third-order triple-frequency wave loads on fixed axisymmetric bodies in monochromatic incident waves. Applying the numerical code, numerical computations were carried out for surge and heave forces and pitch moments on a uniform cylinder, truncated cylinders and a hemisphere. Examinations were made of the contribution to third-order forces and moments from potentials at each wave order, and the relation of third-order forces and moments to wave number and drafts of cylinders.

A Fast Melipole Mechod (FMM) is developed as nurnerical approach to the reduction of tile computauorai cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is dis-crotized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic e-quatiun is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.

A horizontal two-dimensional finite element model is developed in order to estimate the process of scour around a large-scale cylinder due to waves. The present model differs from previous models in the sense that the wave model is based on an elliptic mild slope equation and the sediment transport induced by the steady streaming is considered. The current induced by the gradient of radiation stress is considered and calculated using a depth integrated shallow water equation. The contributions of the Lagrangian drift velocity to the scour is also considered in this model. The model is validated against a few cases where experimental data are available. The comparison of the calculation results with the experimental data indicates that the present numerical model predicts the scour around a large cylinder reasonably well. The effects of Keulegan-Capenter (KC) number, the grain size of sediments and the model scale on scour around a large cylinder are also investigated.